Answer:
Option B and C are correct.
Step-by-step explanation:
Inverse function: If both the domain and the range are R for a function f(x), and if f(x) has an inverse g(x) then:
for every x∈R.
Let and
Use logarithmic rules:
then, by definition;
=
Similarly;
for and
then, by definition;
=
Similarly,
g(f(x)) = x
Therefore, the only option B and C are correct. As the pairs of functions are inverse function.
You can rewrite the inequality as
Note that
is the equation of the line drawn in the pictures. This means that, for every point on the line, the y coordinate is exactly image of the x coordinate, i.e.
The inequality is satisfied by all points whose y coordinate exceeds the image of the x coordinate. Since the y axis is positively oriented upwards, a greater value for the y coordinate means that the point has to be higher than the line.
Also, since the equality inlves a and not a
sign, the line itself is excluded.
So, the correct graph is the second one.