Question

given a function f as f(x)= 5x +4, x is a real number. if g:R→R is inverse of function 'f then what is g(x)

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Answer 1

Answer:

g (x) = ( x - 4)/5

Check the attached image.

Answer 2

$\displaystyle \sf{g(x) = \frac{x - 4}{5} }$

Given :

A function f as f(x) = 5x + 4, x is a real number.

g : R → R is inverse of function

To find :

The function g(x)

Solution :

Step 1 of 2 :

Write down the given function

Here it is given that a function f as f(x) = 5x + 4, x is a real number.

Step 2 of 2 :

Find the function g(x)

Now it is given that g : R → R is inverse of function of f(x)

Then we have

$\displaystyle \sf{ {f}^{ - 1}(x) = g(x) = y \: \: (say) }$

Then f(y) = x

$\displaystyle \sf{ \implies 5y + 4 = x}$

$\displaystyle \sf{ \implies 5y = x - 4}$

$\displaystyle \sf{ \implies y = \frac{x - 4}{5} }$

Hence we have

$\displaystyle \sf{ {f}^{ - 1}(x) = g(x) = \frac{x - 4}{5} }$

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