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If f:RtoR is given by f(x)=3x-5 then f^-...

If `f:RtoR` is given by `f(x)=3x-5` then `f^-1(x)`

A

is given by `(1)/(3x-5)`

B

is given by `(x+5)/(3)`

C

does not exist because `f` is not one-one

D

does not exist because is not onto

Text Solution

Verified by Experts

The correct Answer is:
B
Clearly, `f: R to R` is a one-one onto function, So, it is invertible.
Let f(x)=y. Then,
`3x-5=y Rightarrow x=(y+5)/(3) Rightarrow f^(-1)(y)=(y+5)/(3)`
Hence, `f^(-1)(x)=(x+5)/(3)`
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OBJECTIVE RD SHARMA ENGLISH-FUNCTIONS-Chapter Test
  1. If f:RtoR is given by f(x)=3x-5 then f^-1(x)

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  3. If f(x)=|sin x| then domain of f for the existence of inverse of

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  7. Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) , where m!=n...

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  14. Let f:R to R be a function defined by f(x)=(x^(2)-8)/(x^(2)+2). Then f...

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  15. If f:(-oo,2]to (-oo,4] where f(x), then f ^(-1) (x) is given by :

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  16. Find the inverse of the function, (assuming onto). " " ...

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  17. f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

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  18. If f(x)=log((1+x)/(1-x))a n dt h e nf((2x)/(1+x^2)) is equal to {f(x)...

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  19. If f(x)=(2^x+2^(-x))/2 , then f(x+y)f(x-y) is equals to 1/2{f(2x)+f(2y...

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  20. The function f:R to R given by f(x)=x^(2)+x is

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  21. Let f:R to R and g:R to R be given by f(x)=3x^(2)+2 and g(x)=3x-1 for ...

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