Advertisements
Advertisements
Question
Find fog (2) and gof (1) when : f : R → R ; f(x) = x2 + 8 and g : R → R; g(x) = 3x3 + 1.
Advertisements
Solution
(fog) (2) = f (g (2)) = f (3×23+1) = f(25) = 252 + 8 = 63
(gof) (1) = g (f (1)) = g (12+8) = g (9) = 3×93+1 = 2188
APPEARS IN
RELATED QUESTIONS
Check the injectivity and surjectivity of the following function:
f : R → R given by f(x) = x2
Let f: R → R be defined as f(x) = 10x + 7. Find the function g: R → R such that g o f = f o g = 1R.
Classify the following function as injection, surjection or bijection :
f : Z → Z, defined by f(x) = x2 + x
Show that the function f : R − {3} → R − {2} given by f(x) = `(x-2)/(x-3)` is a bijection.
Let A = [-1, 1]. Then, discuss whether the following functions from A to itself is one-one, onto or bijective : h(x) = x2
If A = {1, 2, 3}, show that a one-one function f : A → A must be onto.
Suppose f1 and f2 are non-zero one-one functions from R to R. Is `f_1 / f^2` necessarily one - one? Justify your answer. Here,`f_1/f_2 : R → R is given by (f_1/f_2) (x) = (f_1(x))/(f_2 (x)) for all x in R .`
Let R+ be the set of all non-negative real numbers. If f : R+ → R+ and g : R+ → R+ are defined as `f(x)=x^2` and `g(x)=+sqrtx` , find fog and gof. Are they equal functions ?
Find fog and gof if : f (x) = x2 g(x) = cos x .
Let f, g, h be real functions given by f(x) = sin x, g (x) = 2x and h (x) = cos x. Prove that fog = go (fh).
if `f (x) = sqrt(1-x)` and g(x) = `log_e` x are two real functions, then describe functions fog and gof.
` if f : (-π/2 , π/2)` → R and g : [−1, 1]→ R be defined as f(x) = tan x and g(x) = `sqrt(1 - x^2)` respectively, describe fog and gof.
Let f be a real function given by f (x)=`sqrt (x-2)`
Find each of the following:
(i) fof
(ii) fofof
(iii) (fofof) (38)
(iv) f2
Also, show that fof ≠ `f^2` .
Consider f : R+ → [−5, ∞) given by f(x) = 9x2 + 6x − 5. Show that f is invertible with `f^-1 (x) = (sqrt (x +6)-1)/3 .`
Consider the function f : R+ → [-9 , ∞ ]given by f(x) = 5x2 + 6x - 9. Prove that f is invertible with f -1 (y) = `(sqrt(54 + 5y) -3)/5` [CBSE 2015]
Let A = {x &epsis; R | −1 ≤ x ≤ 1} and let f : A → A, g : A → A be two functions defined by f(x) = x2 and g(x) = sin (π x/2). Show that g−1 exists but f−1 does not exist. Also, find g−1.
Write the total number of one-one functions from set A = {1, 2, 3, 4} to set B = {a, b, c}.
If f : C → C is defined by f(x) = x4, write f−1 (1).
If f : C → C is defined by f(x) = (x − 2)3, write f−1 (−1).
Write the domain of the real function
`f (x) = sqrtx - [x] .`
Which of the following functions from
to itself are bijections?
Let
\[f : R \to R\] be a function defined by
\[f : R \to R\] is defined by
\[f\left( x \right) = \frac{e^{x^2} - e^{- x^2}}{e^{x^2 + e^{- x^2}}} is\]
If \[g\left( x \right) = x^2 + x - 2\text{ and} \frac{1}{2} gof\left( x \right) = 2 x^2 - 5x + 2\] is equal to
Mark the correct alternative in the following question:
Let f : R → R be given by f(x) = tanx. Then, f-1(1) is
If A = {a, b, c, d} and f = {a, b), (b, d), (c, a), (d, c)}, show that f is one-one from A onto A. Find f–1
If f: R → R is defined by f(x) = x2 – 3x + 2, write f(f (x))
Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not
f = {(1, 4), (1, 5), (2, 4), (3, 5)}
Let X = {1, 2, 3}and Y = {4, 5}. Find whether the following subset of X ×Y are function from X to Y or not
h = {(1,4), (2, 5), (3, 5)}
Let f: R → R be the functions defined by f(x) = x3 + 5. Then f–1(x) is ______.
Let f: R – `{3/5}` → R be defined by f(x) = `(3x + 2)/(5x - 3)`. Then ______.
Let R be a relation on the set L of lines defined by l1 R l2 if l1 is perpendicular to l2, then relation R is ____________.
A function f: x → y is/are called onto (or surjective) if x under f.
'If 'f' is a linear function satisfying f[x + f(x)] = x + f(x), then f(5) can be equal to:
Number of integral values of x satisfying the inequality `(3/4)^(6x + 10 - x^2) < 27/64` is ______.
Let f(n) = `[1/3 + (3n)/100]n`, where [n] denotes the greatest integer less than or equal to n. Then `sum_(n = 1)^56f(n)` is equal to ______.
Let S = {1, 2, 3, 4, 5, 6, 7}. Then the number of possible functions f: S `rightarrow` S such that f(m.n) = f(m).f(n) for every m, n ∈ S and m.n ∈ S is equal to ______.
A function is a rule that assigns each element of one set to exactly how many elements of another set?
A function is onto when every element of the codomain has:
A perfect one-to-one matching between users and unique IDs is similar to:
