Question

Given the function: g (x) = negative one-half x + 3 What is the inverse function of g(x)?

A) f(x) = -2x + 6
B) f(x) = -2x - 6
C) f(x) = 2x + 6
D) f(x) = 2x - 6

Answer 1

Step-by-step explanation:

the inverse function of f(x) gives us for a specified y-value the original x-value that was used in f(x) to get us that y- value.

we can find the inverse function by inverting and transforming the original function from

y = f(x)

into

x = ...

and then we simply rename x to y and y to x to make it a "normal" function.

in our case (if you described it correctly above) the function is named g(x), but the same principles apply.

y = g(x) = -(1/2)x + 3

now we want to transit this into an equation of the form

x = ...

so, we add e.g. (1/2)x to both sides and get

(1/2)x + y = 3

then let's subtract y from both sides

(1/2)x = 3 - y

and then we multiply both sides by 2

x = 6 - 2y or -2y + 6

as last step we rename x to y and y to x

y = g-1(x) = 6 - 2x or -2x + 6

so, A) is correct

Answer 2

The inverse function of g(x) = -½x + 3 is f(x) = -2x + 6, which corresponds to answer choice (A).

Step-by-step explanation:

To find the inverse function of g(x) = -½x + 3, we need to follow these steps:

1. Replace g(x) with y: y = -½x + 3.
2. Interchange the variables x and y: x = -½y + 3.
3. Solve for y, which will give us the inverse function. Multiplying both sides by -2, we get -2x = y - 6. Then, add 6 to both sides: -2x + 6 = y.

Therefore, the inverse function of g(x) is f(x) = -2x + 6, which matches answer choice (A).