MAT1514 Assignment 1 (COMPLETE ANSWERS) 2025

MAT1514 Assignment 1
(COMPLETE ANSWERS) 2025
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, MAT1514 Assignment 1 (COMPLETE
ANSWERS) 2025
Question 1 Given f (x) = 3x2 − 4x + 7 and g(x) =
x2 + 1. Find and simplify the following: apm1514 1.
(g f )(x) (4) 2. (g − f )(x) (2) 3. g f (x) (4) 4. g−1(x)
(3) [13 marks] 2 Downloaded by Corona Virus ()
lOMoARcPSD| MAT1514/101/0/2025
Let's solve each part step by step.
Given functions:
f ( x )=3 x 2−4 x+ 7

g ( x )=x 2+1



1. ( g ∘ f ) ( x ) or g ( f ( x ) )

This means substituting f ( x ) into g ( x ):
g ( f ( x ) )=g ( 3 x −4 x+ 7 )
2



Since g ( x )=x 2+1, replace x with f ( x ):
2
g ( f ( x ) )= ( 3 x −4 x +7 ) +1
2



Expanding the square:
2
( 3 x 2−4 x+7 ) =9 x 4 −24 x 3+ 49 x 2−56 x+ 49
Thus:
g ( f ( x ) )=9 x 4−24 x 3 +49 x 2−56 x +49+1
4 3 2
¿ 9 x −24 x + 49 x −56 x +50



2. ( g−f ) ( x ) or g ( x )−f ( x )
( g−f ) ( x )=g ( x )−f ( x )