Question

Consider the following function. f(x) = 2x + 5. Place the steps for finding f-1 (x) in the correct order. A. x-2/5= y B. y = 2x + 5 C. y-5 = 2x D. X-5/2=y E. f-1(x) = x-5/2 F.x= 2y+ 5 G. x-5= 2y H. f-1(x) = x-2/5

Answer 1

Answer:

$\boxed{\sf \ \ f^{-1}(x)=\dfrac{x-5}{2} \ \ }$

Step-by-step explanation:

hello,

the easiest way to understand what we have to do is the following in my opinion

we can write

$(fof^{-1})(x)=x\\<=>f(f^{-1}(x))=x\\<=>2f^{-1}(x)+5=x\\<=>2f^{-1}(x)+5-5=x-5 \ \ \ subtract \ \ 5\\<=> 2f^{-1}(x)=x-5 \\<=> f^{-1}(x)=\dfrac{x-5}{2} \ \ \ divide \ by \ 2$

so to follow the pattern of your question

y = 2x + 5

we need to find x as a function of y, so let's swap x and y

x = 2y + 5

then subtract 5

x - 5 = 2y

then divide by 2

$\dfrac{x-5}{2}=y$

finally

$f^{-1}(x)=\dfrac{x-5}{2}$

hope this helps

Answer 2

Answer:

1. y= 2x + 5

2. x = 2y + 5

3. x - 5 = 2y

4. (x-5)/2 =u

5. f^-1(x) = (x-5)/2

Step-by-step explanation:

:)