Question

The function f(x) = mx + 5 is its own inverse. Find the value of m?​

Answer 1

mx + 5 = (x - 5) / m

mx + 5 = x/m - 5/mAnswer:

Explanation:

first find the inverse equation

y = mx + 5

y - 5 = mx

(y - 5) / m = x

(x - 5) / m = f⁻ˣ(x)

The original function is a line with slope m and y intercept of 5

The inverse function is a line with a slope 1/m and x intercept of 5

so the common line is where m = 1/m

m = 1/m

m² = 1

m = ± 1

The only line with a common slope between these two options is when

m = -1 and y intercept is 5