MathDB

Function convolution

Source: 2014-2015 SDML High School 1a Problem 6/2014-2015 SDML Middle School 1a Problem 12

August 28, 2016

functionreal analysis2014-15 SDML Round 1SDML High SchoolSDML Middle School

Problem Statement

Let

f\left(x\right)=x^2-14x+52

and

g\left(x\right)=ax+b

, where

a

and

b

are positive. Find

a

, given that

f\left(g\left(-5\right)\right)=3

and

f\left(g\left(0\right)\right)=103

\text{(A) }2\qquad\text{(B) }5\qquad\text{(C) }7\qquad\text{(D) }10\qquad\text{(E) }17