Question

Consider the function. Which conclusions can be drawn about f–1(x)? Select two options. F–1(x) has a slope of. F–1(x) has a restricted domain. F–1(x) has a y-intercept of (0, –36). F–1(x) has an x-intercept of (–36, 0). F–1(x) has a range of all real numbers.

Answer 1

The required function is $y = -\frac{3}{2} x -36$ having domain and range as R and y-intercept is -36.

Given function

y=f(x) = $-\frac{2}{3} x -24$

What is an inverse function?

An inverse function is a function that returns the original value for which a function has given the output. If f(x) is a function that gives output y, then the inverse function of y, i.e. f-1(y) will return the value x.

In order to get inverse function $f^-1x$ let us arrange the given function

$y+24 = -\frac{2}{3} x$

$x = -\frac{3}{2} y-36$

Now, replace x with y and vice versa.

$y = -\frac{3}{2} x -36$........(1)

or, $f^-1x = -\frac{3}{2} x -36$

(1) will be the inverse function of the given function.

For x-intercept put y = 0 and for y-intercept put x=0 in eq(1)

x-intercept = -24

y-intercept = -36

The domain and range of f⁻¹x = set of all real numbers since f⁻¹x is a straight line equation, domain, and range of which is set of all real numbers.

Therefore, the required function is $y = -\frac{3}{2} x -36$ having domain and range as R and y-intercept is -36.

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