Match each function with its inverse function. Use function composition to determine your answers.
Please help

Answer:

For f(x) =  x^2 - 2x + 1, the inverse is g(x) = √x + 1

For f(x) = 2 - 5*x the inverse is g(x) = (2 - x)/5

For f(x) =  5*(x - 2) the inverse is g(x) = x*(1/5) + 2

for f(x) = (x - 2)^2 - 1 the inverse is g(x) = √(x + 1) + 2

Step-by-step explanation:

If we have two functions f(x) and g(x) such that these functions are inverse, then we have:

f( g(x)) = x

and

g( f(x)) = x

Let's start with the function:

f(x) = x^2 - 2x + 1

Notice that we can rewrite this as:

f(x) = x^2 - 2*x + 1 = (x - 1)^2

Because this is a quadratic function, the inverse function needs to have a square root, then the inverse function can be the third or fourth one.

Let's try with the last one:

g(x) = √x + 1

Then:

f( g(x)) = ( √x + 1 - 1)^2 = (√x )^2 = x

g( f(x)) = √(x - 1)^2 + 1 = (x - 1) + 1 = x

Then for the function:

f(x) = x^2 - 2x + 1, the inverse is: g(x) = √x + 1

Now let's find the inverse for the second function:

f(x) = 2 - 5*x

The inverse of this function will be also a linear function, and the slope of the inverse will be the inverse of this slope, then the inverse may be the first or second options.

Let's try with:

g(x) = (1/5)*x - 2

Then:

f( g(x) ) = 2 - 5*((1/5)*x - 2) = 2 - x + 10

Then this g(x) is not the inverse of the function.

Let's try with g(x) = (2 - x)/5

Then:

f( g(x)) = 2 - 5*(2 - x)/5 = 2 - 2 + x = x

g( f(x)) =  (2 - 2 - 5*x)/5 = 5*x/5 = x

For the function f(x) = 5*(x - 2)

The inverse should be the remaining linear function:

g(x) = x*(1/5) + 2

Then:

f( g(x)) = 5*(x*(1/5) + 2 - 2) = 5*x*(1/5) = x

g( f(x)) = (5*(x - 2) )*(1/5) + 2 = (x - 2) +2 = x

For the last function, f(x) = (x - 2)^2 - 1

The inverse function will be:

g(x) = √(x + 1) + 2

The compositions are:

f( g(x)) = (√(x + 1) + 2 - 2)^2 - 1 = (√(x + 1))^2 - 1 = (x + 1) - 1 = x

g(f(x)) = √((x - 2)^2 - 1 + 1) + 2 = √((x - 2)^2 + 2 = x

Answer:

PLATO ANSWER

Step-by-step explanation:

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