Advertisements
Advertisements
प्रश्न
If f : R → R, f(x) = x3 and g: R → R , g(x) = 2x2 + 1, and R is the set of real numbers, then find fog(x) and gof (x)
Advertisements
उत्तर
f : R → R and g : R → R
∴ f (g(x)) and g(f(x)) both are defined over common domain
f(g(x))= (g(x))3 = (2x2 + 1)3
= 8x6 + 12x4 + 6x2 + 1
g(f (x)) = 2(f(x))2 + 1 = 2(x3)2 + 1 = 2x6 + 1
APPEARS IN
संबंधित प्रश्न
If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x3 + 5, then find the value of (fog)−1 (x).
Consider f: R+ → [–5, ∞) given by f(x) = 9x2 + 6x – 5. Show that f is invertible with `f^(-1)(y) = ((sqrt(y + 6) - 1)/3)`.
Let f: X → Y be an invertible function. Show that the inverse of f−1 is f, i.e., (f−1)−1 = f.
Consider f: `R_+ -> [-5, oo]` given by `f(x) = 9x^2 + 6x - 5`. Show that f is invertible with `f^(-1) (y) ((sqrt(y + 6)-1)/3)`
Hence Find
1) `f^(-1)(10)`
2) y if `f^(-1) (y) = 4/3`
where R+ is the set of all non-negative real numbers.
Let f: A → B and g: B → C be the bijective functions. Then (g o f)–1 is ______.
Let f: [0, 1] → [0, 1] be defined by f(x) = `{{:(x",", "if" x "is rational"),(1 - x",", "if" x "is irrational"):}`. Then (f o f) x is ______.
Let f: N → R be the function defined by f(x) = `(2x - 1)/2` and g: Q → R be another function defined by g(x) = x + 2. Then (g o f) `3/2` is ______.
Let f: R → R be the function defined by f(x) = sin (3x+2) ∀ x ∈ R. Then f is invertible.
The composition of functions is commutative.
The composition of functions is associative.
Let f : R → R be the functions defined by f(x) = x3 + 5. Then f-1(x) is ____________.
If f : R → R defind by f(x) = `(2"x" - 7)/4` is an invertible function, then find f-1.
Domain of the function defined by `f(x) = 1/sqrt(sin^2 - x) log_10 (cos^-1 x)` is:-
If `f(x) = 1/(x - 1)`, `g(x) = 1/((x + 1)(x - 1))`, then the number of integers which are not in domian of gof(x) are
Which statement correctly describes an onto (surjective) function?
If \(f:A\to B\) and \(g:B\to C\) are both bijections, which statement is the Reversal Law of Inverses?
Which pair consists of examples of self-inverse functions?
For \(f(x)=4x+3\), where \(Y=\{y\in\mathbb{N}:y=4x+3\text{ for some }x\in\mathbb{N}\}\), what is the inverse function \(g:Y\to\mathbb{N}\)?
For \(f:\mathbb{R}\to(-1,1)\) defined by \(f(x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}\), what is \(f^{-1}(x)\)?
What are the domain and range of the inverse function in the graphical example?
