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ANSWER

[tex] \boxed {m \ne0}[/tex]



EXPLANATION


The given function is

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


We need to find the inverse of this function,



Let

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


We interchange x an y to obtain,


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


We solve for y now to obtain,


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


We divide through by m to get,

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


Hence the inverse function is ,


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


For this inverse to exist, the denominator must not be equal to zero,

Thus

[tex]m \ne0[/tex]


The correct answer is A.

Answer:

Option 1 m≠0 is the right option.

Step-by-step explanation:

In this question we will find the inverse function first then we will find the gradient of the inverse function to get the correct answer.

The given function is f(x) = mx + b

Or y = mx + b

Now we will rewrite the equation in the form of x.

y - b = mx + b - b

y - b = mx

[tex]x = \frac{1}{m}y - \frac{b}{m}[/tex]

Now we can write the inverse function as

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

Now the gradient of the inverse function is (1/m).Therefor we can easily say that the given function is defined when m≠0 because for m = 0 gradient will be infinity.

Therefore option 1. m≠0 is the right option.

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