MAT1514 Assignment 1 (COMPLETE ANSWERS) 2025 - DUE 2025; 100% TRUSTED Complete, trusted solutions and explanations. Ensure your success with us.

Question 1 1.1 Find and simplify 𝑔 ( 𝑓 ( 𝑥 ) ) g(f(x))
We are given 𝑓 ( 𝑥 )
2 𝑥 + 15 f(x)=2x+15, but 𝑔 ( 𝑥 ) g(x) is not clearly defined. If you provide 𝑔 ( 𝑥 ) g(x), I
can complete the solution.


1.2 Solve for 𝑥 x 2 𝑒 − 𝑥 − 1

0 2e −x −1=0 Add 1 to both sides: 2 𝑒 − 𝑥

1 2e −x =1 Divide by 2: 𝑒 − 𝑥

1 2 e −x
21


Take the natural logarithm on both sides: − 𝑥
ln ⁡1 2 −x=ln 2 1

, Since ln ⁡1 2

− ln ⁡2 ln 2 1 =−ln2, we get: 𝑥

ln ⁡2 x=ln2 1.3 Solve for 𝑥 x ln ⁡𝑒 𝑥 + ln ⁡5

ln ⁡25 lne x +ln5=ln25 Using ln ⁡𝑒 𝑥

𝑥 lne x =x, rewrite: 𝑥 + ln ⁡5

ln ⁡25 x+ln5=ln25 Since ln ⁡25

ln ⁡5 2

2 ln ⁡5 ln25=ln5 2 =2ln5, we get: 𝑥 + ln ⁡5

2 ln ⁡5 x+ln5=2ln5 Solve for 𝑥 x: 𝑥

ln ⁡5 x=ln5 1.4 Solve for 𝑥 x log ⁡8 + log ⁡( 7 − 4 𝑥 )

log ⁡5 log8+log(7−4x)=log5 Use log ⁡𝐴 + log ⁡𝐵

log ⁡( 𝐴 ⋅ 𝐵 ) logA+logB=log(A⋅B): log ⁡[ 8 ( 7 − 4 𝑥 ) ]

log ⁡5 log[8(7−4x)]=log5 Cancel logs: 8 ( 7 − 4 𝑥 )

5 8(7−4x)=5 Expand: 56 − 32 𝑥