Let be defined by

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let

f\!:\!\mathbb R \to (0,\infty)

be defined by

f(x)=e^{x}+4

. Decide whether

f

is onto its codomain. (a) Yes, because

e^{x}

can take all positive values. (b) Yes, because for every

y>0

x=\ln(y-4)

satisfies

f(x)=y

. (So every positive

y

is attained.) (c) No, because the range of

f

(4,\infty)

. (d) No, because the range of

f

[4,\infty)