Question

Which function represents the inverse function of the function f(x)= x^2+5

Answer 1

The inverse function : $f^{-1}(x)=\sqrt{x-5}$

Further explanation

A ƒunction can be expressed in the form of a cartesian diagram, sequential pairs, or arrow diagrams  

If a ƒunction (f) pairs members of set A to set B, then the inverse of ƒunction f (f⁻¹) pairs members of set B to A, or easily f⁻¹ is the opposite of f  

or in the form of equations  :

f (x) = y if and only if g (y) = x  

g (y) is called the inverse of f (x)  

The step for determining the inverse ƒunction  

1. expresses the ƒunction y = f (x) in the form x = f (y)  

2. f⁻¹(y) = g(y)  

3. Replace the letter y with x so we get the inverse ƒunction formula f⁻¹(x)  

Known :  

f (x) =x² +5  

suppose f (x) = y then  

y = x² +5  

x ² = y-5

$\displaystyle x=\sqrt{y-5}\\\\f^{-1}(y)=\sqrt{y-5}\\\\f^{-1}(x)=\sqrt{x-5}$

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Answer 2

Answer:

$f^{-1}(x)=(+/-)\sqrt{x-5}$

Step-by-step explanation:

we have the function

$f(x)=x^{2} +5$

Let

$y=f(x)$

$y=x^{2} +5$

step 1

Exchange the variables, x for y and y for x

$x=y^{2} +5$

step 2

Isolate the variable y

Subtract 5 both sides

$x-5=y^{2}$

step 3

Take square root both sides

$y=(+/-)\sqrt{x-5}$

step 4

Find the inverse

$f^{-1}(x)=y$

so

$f^{-1}(x)=(+/-)\sqrt{x-5}$