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meerkat18
The inverse function of the function f(x) = mx + b can be determined by expressing the function in terms of x alone. hence, (y - b)/m = x. Then we exhange x and y, to result to (x - b)/m = y. In this case, m is not equal to zero. The answer to this problem hence is A>
calculista

we have

[tex]f(x)=mx+b[/tex]

Find the inverse of f(x)

Let

[tex]y=f(x)[/tex]

[tex]y=mx+b[/tex]

Exchanges the variables x for y and y for x

[tex]x=my+b[/tex]

isolate the variable y

[tex]my=x-b[/tex]

[tex]y=\frac{x-b}{m}[/tex]

Let

[tex]f(x)^{-1} =y[/tex]

[tex]f(x)^{-1}=\frac{x-b}{m}[/tex] -----> inverse function

Hence

In the inverse function the denominator can not be zero, therefore the value of m can not be equal zero

the answer is the option

[tex]m\neq 0[/tex]

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