Does anyone know how to do this Pre-Calculus proof?

Question

Prove that f(x)=((x-3)^(3))+4 and g(x)=((x-4)^(1/3))+3 are inverse functions.

Answer 1

By definition of "inverse functions", f(x) and g(x) are inverse functions if and only if f(g(x)) = g(f(x)). It has nothing to do with reciprocals, as somebody else suggested.

So take the f(x) expression and plug the entire thing into the g(x) expression for x. You should end up getting x back. Then take the original g(x) expression and plug it into f(x). You should end up with the same result, x. This proves f(g(x)) = g(f(x)) for all x.

Answer 2

The sine and cosine graphs both have optimal and minimum amplitudes at a million and -a million. The cosine graphs is an actual translation of the sine graph shited alongside 90degrees (pi/2; pi is 180degrees). that's at 0 stages sin=0, cosin=a million. Sine and cosine are cofunctions of one yet another. therefore that, at the same time as A and B are complementary angles (meaning at the same time as both angles A and B upload as a lot as 90degrees, so A would opt to be 10, B would opt to be 80 and so that they could be complementary) sinA = cosB.

Answer 3

Replace x in the definition of f(x) with the definition of g(x), and vice versa. If both expressions come out to equal x, then it's proved.

Answer 4

Substitute a value for x in both equations that is the same. The answers will become reciprocals of each other.