Question

The graphs f of x equals 4 x and g of x equals 4 Superscript x Baseline intersect at x equals 1-half and x equals 1.



Select ,begin emphasis,all,end emphasis, of the intervals of x for which g of x is greater than f of x.

Answer options with 6 options
A.
left-parenthesis negative infinity comma infinity right-parenthesis

B.
left-parenthesis negative infinity comma 1-half right-parenthesis

C.
left-parenthesis negative infinity comma 1 right-parenthesis

D.
left-parenthesis 1-half comma 1 right-parenthesis

E.
left-parenthesis 1-half comma infinity right-parenthesis

F.
left-parenthesis 1 comma infinity right-parenthesis

Answer 1

B and F.

Reason: Let h(x)=4^x−4x. h(1/2)=h(1)=0. For x=0 (in (−∞,1/2)) h(0)=1>0, so 4^x>4x on (−∞,1/2). For x=3/4 (in (1/2,1)) h(3/4)≈2.828−3<0, so 4^x<4x there. For x=2 (in (1,∞)) h(2)=16−8>0, so 4^x>4x on (1,∞). Thus intervals are (−∞,1/2) and (1,∞) — options B and F.