Answer:
y = 1/4 x - 5/4
Step-by-step explanation:
y = 4x + 5
Switch x and y.
x = 4y + 5
Solve for y.
4y = x - 5
y = 1/4 x - 5/4
The inverse of the function y = 4x + 5 is [tex]f^{-1}(x) = \frac{x-5}{4}[/tex]
The given function is:
y = 4x + 5
To find the inverse of the given function y = 4x + 5, follow the following steps:
Make x the subject of the formula:
[tex]y = 4x + 5\\\\4x = y - 5\\\\x = \frac{y}{4}-\frac{5}{4}[/tex]
Replace x by [tex]f^{-1}(x)[/tex] and replace y by x.
The resulting function represents the inverse of the function y = 4x + 5
[tex]f^{-1}(x)=\frac{x}{4}-\frac{5}{4}[/tex]
Which can be further simplified as:
[tex]f^{-1}(x) = \frac{x-5}{4}[/tex]
The inverse of the function y = 4x + 5 is [tex]f^{-1}(x) = \frac{x-5}{4}[/tex]
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