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If f: R->R is defined by f(x)=10 x-7 , t...

If `f: R->R` is defined by `f(x)=10 x-7` , then write `f^(-1)(x)` .

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Let `f^{-1}(x)=y`

`Rightarrow {f}({y})={x}`

It is given that, `{f}({x})=10 {x}-7`, then `{f}({y})=10 {y}-7`.

`Rightarrow 10 {y}-7={x}`

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RD SHARMA-FUNCTION-Solved Examples And Exercises
  1. If f: R->R is defined by f(x)=x^2 , write f^(-1)(25) .

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  2. If f: C->C is defined by f(x)=(x-2)^3 , write f^(-1)(-1) .

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  3. If f: R->R is defined by f(x)=10 x-7 , then write f^(-1)(x) .

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  4. Let f:{-pi/2,\ pi/2}->R be a function defined by f(x)=cos[x]dot Write ...

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  5. If f: R->R defined by f(x)=3x-4 is invertible then write f^(-1)(x) .

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  6. If f: R->R , g: R->R are given by f(x)=(x+1)^2 and g(x)=x^2+1 , then w...

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  7. Let A={x in R :-4lt=xlt=4 and x!=0} and f: A->R be defined by f(x)=(|...

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  8. Let f:[-pi/2,\ pi/2]->A be defined by f(x)=sinx . If f is a bijection,...

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  9. Let f: R->R^+ be defined by f(x)=a^x ,\ a >0 and a!=1 . Write f^(-1)(x...

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  10. Let f: R-{-1}->R-{1} be given by f(x)=x/(x+1) . Write f^(-1)(x) .

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  11. Let f: R-{-3/5}->R be a function defined as f(x)=(2x)/(5x+3) . Write f...

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  12. Let f: R->R , g: R->R be two functions defined by f(x)=x^2+x+1 and g(x...

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  13. Let f: R->R be defined as f(x)=(2x-3)/4 . Write fof^(-1)(1) .

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  14. Let f be an invertible real function. Write (f^(-1)\ of)(1)+(f^(-1)...

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  15. Let A={1,\ 2,\ 3,\ 4} and B={a ,\ b} be two sets. Write total numbe...

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  16. Write the domain of the real function f(x)=sqrt(x-[x]) .

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  17. Write the domain and range of function f(x) given by f(x)=sqrt([x]-x)d...

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  18. Write the domain of the real function f(x)=1/(sqrt(|x|-x))

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  19. Write whether f: R->R given by f(x)=x+sqrt(x^2) is one-one, many-one, ...

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  20. If "f"("x")=x+7 and g(x)=x-7,\ x\ \ R , find (fog)(7)

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