for the functions f(x) = 5x +50 and g(x) = 1/5x -10 evaluate both f(g(x)) and g(f(x)). Are these functions inverses?

do you put them into each other?

To evaluate functions composed of other functions, you need to substitute the inner function into the outer function and simplify the expression.

Let's start by evaluating f(g(x)). To do this, substitute g(x) into the function f(x):

f(g(x)) = 5(g(x)) + 50

Now, substitute the expression for g(x) (which is 1/5x - 10) into the equation above:

f(g(x)) = 5[(1/5x - 10)] + 50

Simplify the equation:

f(g(x)) = 1x - 50 + 50

f(g(x)) = x

Now, let's evaluate g(f(x)). To do this, substitute f(x) into the function g(x):

g(f(x)) = (1/5)f(x) - 10

Substitute the expression for f(x) (which is 5x + 50) into the equation above:

g(f(x)) = (1/5)(5x + 50) - 10

Simplify the equation:

g(f(x)) = x + 10 - 10

g(f(x)) = x

Both f(g(x)) and g(f(x)) simplify to x, indicating that they are equal to the identity function. This means they are inverse functions of each other.

To determine if two functions are inverses of each other, you should check if the composition of the functions simplifies to the identity function, as shown above.

f(x) = 5x+50

g(x) = x/5 - 10

f(g(x)) = 5(x/5-10) + 50
= x - 50 + 50 = x

g(f(x) = (5x+50)/5 - 10
= x + 10 - 10 = x

Yup they are

check:
let f(x) = 5x+50 be written as
y = 5x+50
to form the inverse, interchange the x and y
x = 5y + 50
now solve this for y
5y = x - 50
y = x/5 - 10

I was right.