The inverse of f(x) = 4x + 5 is:
[tex]g(x) = (1/4)*x - 5/4[/tex]
How to get the inverse of f(x)?
Two functions f(x) and g(x) are inverses if and only if:
[tex]f(g(x)) = x\\\\g(f(x)) = x[/tex]
If f(x) = 4x + 5.
Then the inverse is also a linear function:
g(x) = a*x + b
When we compose f(x) and g(x) we must get:
[tex]f(g(x)) = 4*g(x) + 5 = 4*(a*x + b) + 5 = x\\\\4ax + (4b + 5) = x[/tex]
From that we get two equations:
4a = 1
4b + 5 = 0
Then:
a = 1/4
b = -5/4
So the inverse of f(x) is:
[tex]g(x) = (1/4)*x - 5/4[/tex]
If you want to learn more about inverses:
https://brainly.com/question/14391067
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