Question

Which of the following statements is not always true ?

a. if a function contains the origin , then its inverse contains the origin.
b.if a function has 3 x-intercepts, then its inverse has 3 y-intercepts.
c.if a function contains no points in the fourth quadrant, then its inverse contains no points in the second quadrant.
d.if the slope of a linear function is less than 1, then the slope of its inverse is greater than 1.,

Answer 1

Ans. C We know, when an inverse function is generated, the graph of the parent function gets reversed as a mirror image with mirror on y=x line. A, B and D are hence always true. In C, there's no such rule. Even if fourth quadrant doesn't contain a point, second may or may not. Example y =2^x doesn't have any point in fourth quadrant but its inverse y=log x,base 2 has points in second quadrant.