Question

Which statement must be true? a b c d

Answer 1

ANSWER

$\boxed {m \ne0}$



EXPLANATION


The given function is

$f(x) = mx + b$


We need to find the inverse of this function,



Let

$y= mx + b$


We interchange x an y to obtain,


$x = my + b$


We solve for y now to obtain,


$x - b = my$


We divide through by m to get,

$\frac{x - b}{m} = y$


Hence the inverse function is ,


${f}^{ - 1} (x) = \frac{x - b}{m}$


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

Thus

$m \ne0$


The correct answer is A.

Answer 2

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

$x = \frac{1}{m}y - \frac{b}{m}$

Now we can write the inverse function as

$f^{-1}(x) = \frac{x}{m} - \frac{b}{m}$

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.