Question

If f(x)=5x+3,find f power -1

Answer 1

Answer:

(x-3)/5

☸Given☸

f(x)=5x+3

To Find:

• Value of $\bf{f^{-1}(x)}$

✯Solution✯

Following are the steps to find inverse of function:

• First let the function be equal to y i.e. f(x)=y.
• Then find the value of x in terms of y i.e. x=f(y)
• Now, by substituting y with x in f(y), the obtained f is the required inverse of function i.e. f(y⇒x)=$\sf{f^{-1}(x)}$.

☛ Now, going with steps let us find inverse of given function

$\longrightarrow\sf{f(x)=y}$

$\longrightarrow\sf{5x+3=y}$

$\longrightarrow\sf{5x=y-3}$

$\longrightarrow\sf{x=\dfrac{y-3}{5}}$

$\longrightarrow\sf{x=f(y),\:where\:f(y)=\dfrac{y-3}{5}}$

Now, on substituting y with x, we get

$\longrightarrow\sf{\pink{f^{-1}(x)=\dfrac{x-3}{5}}}$

Hence, the value of $\bf{\purple{f^{-1}(x)}}$ is $\bf{\green{\dfrac{x-3}{5}}}$.

Answer 2

Given:

f(x)=5x+3

To Find:

Value of 

$\sf{f ^{ - 1} }$

✯Solution✯

Following are the steps to find inverse of function:

• First let the function be equal to y i.e. f(x)=y.

• Then find the value of x in terms of y i.e. x=f(y)

• Now, by substituting y with x in f(y), the obtained f is the required inverse of Function.

☛ Now, going with steps let us find inverse of given function

$\sf{f(x) = y } \\ \sf{5x + 3 = y} \\ \sf{5x = y - 3} \\ \sf{x = \frac{y - 3}{5} } \\ \sf{x = f(y) \: \: where \: f(y) = \frac{y - 3}{5} } \\ \sf{ \implies \: f ^{ - 2} (x) = \frac{x - 3}{5}}$