We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# How can i find the inverse of this function?

0
361
1

How can I find the inverse of f^-1? Oct 9, 2017

### 1+0 Answers

#1
+1

$$f(x)=\sqrt{5-x}+3$$

Changing this to its inverse requires a few steps.

1. Change $$f(x)$$ to $$y$$.

This step is pretty simple. We are switching from function notation to y=-notation. $$f(x)=\sqrt{5-x}+3$$ changes to $$y=\sqrt{5-x}+3$$

2. Interchange x and y

This step is also quite simple; replace all instances of x with y and all instance of y with x.

$$y=\sqrt{5-x}+3$$ changes to $$x=\sqrt{5-y}+3$$

3. Solve for y

This step is the hardest. Transform the equation into the form of y=.

 $$x=\sqrt{5-y}+3$$ Subtract 3 on both sides. $$x-3=\sqrt{5-y}$$ Square both sides to eliminate the square root. $$(x-3)^2=\left(\sqrt{5-y}\right)^2$$ Expand the left hand side knowing that $$(a-b)^2=a^2-2ab+b^2$$. $$x^2-6x+9=5-y$$ Subtract 5 from both sides. $$-y=x^2-6x+4$$ Divide by -1. $$y=-x^2+6x-4$$

4. Consider Whether the Inverse is actually a Function

In this case, it is a function, so we are OK.

Oct 9, 2017