1953 AMC 12 Problem 38

Attempt Problem 38 of the 1953 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1953 AMC 12 solutions, or check the answer key.

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38.

If

f(a)=a-2

and

F(a,b)=b^2+a,

then

F[3,f(4)]

is:

a^2-4a+7

28

7

8

11

Answer: C

Concepts:function notation composition substitution

Difficulty rating: 1390

Small hint:

Evaluate the inner function

f(4)

first

Big hint:

Then substitute

a=3

and the resulting value for

b

into

F(a,b)

Solution:

First

f(4)=4-2=2.

Therefore

\begin{aligned} F[3,f(4)]&=F(3,2)\\ &=2^2+3=7. \end{aligned}

Thus, the correct answer is C.

Problem 38 in other years