Question

Which of the following statements about f(x) is true?

A. The function f(x) does not have an inverse because it never crosses the x-axis.


B. The function f(x) has an inverse because it passes the horizontal line test.


C. The function f(x) does not have an inverse because it does not pass the horizontal line test.


D. The function f(x) has an inverse because it passes the vertical line test.

Answer 1

The correct answer is b) the function has an inverse because if passes the horizontal line test.

Answer 2

B. The function f(x) has an inverse because it passes the horizontal line test.

Explanation:

The given function is the graph of
`f(x)=((5)/(4))^x+1`.

This function will have an inverse if and only if its graph passes the horizontal line test.

That is, if a horizontal line is drawn across the graph, it will intersect the graph at only one point.

Since the graph of the given function passes the horizontal line test, it has an inverse.

See graph in attachment.

The correct answer is B.