Question

Hi,i can’t upload attachment but the question says the graph of f(x)=square root -x+2 and h(x)= 2 to the power of x then -1.The graph of f(x) has a restricted domain.Then they drew a graph of these functions,now they ask:
1)For what values of x is h(x)=f(x)+3?
2)For what values of x is h(x) . f prime x smaller than and equal to 0?

How do I do these questions,do I have to calculate or where do I start?Please help me,I’m very confused.Thanks

Answer 1

I will try to explain on the graph.

1) you have to find x for which exists h (x)=2^x-1. On my chart, it's blue color. The graph of the new function h(x)=f(x)+3 is drawn in black. As you can see, the values of x are the same, the differences are only in the value of y. thus, the graph h (x)=f(x)+3 exists for x (- infinity, 2).

2) look at the graph and see that f (x)<=0 on the plot green color for x is (- infinity, 0]