Advertisements
Advertisements
Question
If f(x) = `((x + 1)/(x - 1))`, then prove that f(f(x)) = x.
Advertisements
Solution
f(x) = `((x + 1)/(x - 1))`
f(f(x)) = `((x + 1)/(x - 1) + 1)/(((x+1)/(x-1)) - 1)`
`= ((x + 1 + (x - 1)!)/(x-1))/(((x+1)-(x-1))/(x-1))`
`= (x+1+x-1)/(x+1-x+1)`
`(2x)/2` = x
Hence proved.
APPEARS IN
RELATED QUESTIONS
Determine whether the following function is odd or even?
f(x) = x + x2
If f(x) = `x^3 - 1/x^3`, then show that `"f"(x) + "f"(1/x)` = 0
For f(x) = `(x - 1)/(3x + 1)`, write the expressions of `"f"(1/x) and 1/("f"(x))`
Draw the graph of the following function:
f(x) = e-2x
Draw the graph of the following function:
f(x) = `|x|/x`
If f(x) = `{(x^2 - 4x if x >= 2),(x+2 if x < 2):}`, then f(5) is
The graph of the line y = 3 is
The graph of y = 2x2 is passing through:
The graph of y = ex intersect the y-axis at:
If f(x) = 2x and g(x) = `1/2^x` then (fg)(x) is:
