f(x), g(x) and h(x) are defined for x N as follows:
f(x)= 3x + 2, g(x)= 4x + 1, h(x)= 5x + 3.
which of the following can be expressed as all the three functions f, g and h
A. 30x + 17
B. 60x + 41
C. 30x + 13
D. 60x + 53
Answers
30x + 17 = 2f(x) + g(x) + 4h(x) , 30x + 13 = 3f(x) + 4g(x) + h(x) if f(x)= 3x + 2, g(x)= 4x + 1, h(x)= 5x + 3
Step-by-step explanation:
a * f(x) + bg(x) + c h(x)
= a( 3x + 2) + b(4x + 1) + c(5x + 3)
= x(3a + 4b + 5c) + 2a + b + 3c
Equating with 30x + 17
3a + 4b + 5c = 30 Eq1
2a + b + 3c = 17 Eq2
4 * eq2 - Eq1
=> 5a + 7c = 38
c = 4 a = 2
2 (2) + b + 3(4) = 17
=> b = 1
30x + 17 = 2f(x) + g(x) + 4h(x)
Similarly for 60x + 41
3a + 4b + 5c = 60 Eq3
2a + b + 3c = 41 Eq4
4 * eq4 - Eq3
=> 5a + 7c = 104
a = 18 c = 2 => b = -1
a = 4 c = 12 => b = -3
( not considering -ve Values)
Similarly for 30x + 13
3a + 4b + 5c = 30 Eq5
2a + b + 3c = 13 Eq6
4 * eq6 - Eq5
=> 5a + 7c = 22
a = 3 c = 1 => b = 4
=> 30x + 13 = 3f(x) + 4g(x) + h(x)
Similarly for 60x + 53
3a + 4b + 5c = 60 Eq7
2a + b + 3c = 53 Eq8
4 * eq8 - Eq7
=> 5a + 7c = 152
a = 29 c = 1 => b = -8
a = 15 c = 11 => b = -10
a = 1 c = 21 => b = -12
( not considering -ve Values)
Learn More:
If f(x)=4x, g(x)=5x-3 and h(x)=sqrt of x, find (fogoh)(4) -
https://brainly.in/question/5851881
If the polynomial f(x)=px^3+4x^2+3x-4 and g(x)=x^3-4+p are divided ...
https://brainly.in/question/3984836