Home
Class 12
MATHS
Let f:R to R, g: R to R be two functions...

Let `f:R to R, g: R to R` be two functions given by `f(x)=2x-3,g(x)=x^(3)+5`. Then `(fog)^(-1)` is equal to

A

`((x+7)/(2))^(1//3)`

B

`(x-(7)/(2))^(1//3)`

C

`((x-2)/(7))^(1//3)`

D

`((x-7)/(2))^(1//3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`f : R rarr R`
g : R `rarr` R
f(x) = 2x - 3
`g(x) = x^(3) + 5`
implies `(fog)(x)=f(g(x))=f(x^(3)+5)=2(x^(3)+5)-3`
`=2x^(3)+7`
Now, let `y = 2x^(3) + 7`
`2x^(3) = y - 7`
`x=((y-7)/(2))^(1//3)`
Replacing x by y, we get
`y=((x-7)/(2))^(1//3)`
`therefore (fog)^(-1)(x)=((x-7)/(2))^(1//3)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Let f : R to R be a function defined by f(x) = 4x - 3 AA x in R . Then Write f^(-1) .

If f: R to R and g: R to R are given by f(x)= cosx and g(x) =3x^(2) .Show that gof ne fog

Let f : R rarr R be a function defined by f(x) = x^3 + 5 . Then f^-1(x) is

For x in R , the functions f(x) satisfies 2f(x)+f(1-x)=x^(2) . The value of f(4) is equal to

Let f,g: RrarrR be two functions defined as f(x)=|x|+x and g(x)=|x|-xAAx in R . Then f(g) (x) for xlt0 is

Let f, g : R rarrR be two functions defined as f(x) = |x| + x and g(x) = | x| - x AA x in R. . Then (fog ) (x) for x lt 0 is

Let f : R to R be defined by f(x)=x^(4) , then