questions on inverse functions?

Question

Are the pairs of functions are inverse functions: f(x) = -5x + 1 and g(x) = 1/5(1-x)?

Find the inverse function of the following: f(x) = 3 - 1/2x

Find the inverse function of the following: f(x) = 4x + 2

Answer 1

'Are the pairs of functions are inverse functions: f(x)= -5x + 1 and g(x) = 1/5 (1 - x)

Answer: Yes, they are inverse.

If you want to find the the inverse of f(x) = -5x + 1, instead of "x." You replace the "x" with "y."

Example: x = -5y + 1. Your job is find the y-value equation. You subtract the +1 to "x."

So it looks like this: x - 1 = -5y.

Then you divide the -5 to x - 1. Your y-value equation looks like this: -1/5x + 1/5.

The answer is: Yes, the pairs of functions are inverse functions.



2) Find the inverse function of the following: f(x) = 3 - 1/2x. You do the same as the first question. Replace the "x" with "y".

Like this: x = 3 - 1/2y

The inverse function will be y = -2x + 6 <---Answer

3) Replace the "x" with "y." x = 4y + 2

Answer y = 1/4x - 1/2

Answer 2

Use the composition to determine is they are inverses:



f(g(x)) = f((1/5)(1 - x)) = -5(1/5)(1 - x) + 1 = -(1 - x) + 1 = -1 + x - 1 = x

g(f(x)) = g(-5x + 1) = (1/5)(1 - (-5x + 1)) = (1/5)(1 + 5x - 1) = (1/5)(5x) = x

these functions are inverses





Replace f(x) with y: y = 3 - (1/2)x

Interchange x and y; x = 3 - (1/2)y

Solve for y: x - 3 = -(1/2)y --> -2(x - 3) = y this should be the inverse, now verify





y = 4x + 2

x = 4y + 2

x - 2 = 4y

(1/4)(x - 2) = y

Answer 3

To find an inverse of a function is to interchange x and f(x) = y and solve for y

i.e.

f(x) = 4x + 2 = y: So, x = 4y + 2 or y = (x - 2) / 4 = f ^( - 1) (x)



Hence, the inverse function of f(x) = 4x + 2 is f ^( - 1) (x) = (x - 2) / 4

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Hope this helps!