Question

Use functions a(x)= 4x+9 and b(x)= 3x-5
A: find (a+b) (x)
B: find (a-b) (x)
C: find a[b(x)]

Please help, this is my final and I need to pass to graduate next week! I genuinely have no idea what I am doing

Answer 1

The sum/difference of two functions is simply defined as the sum between their expression:

$(f\pm g)(x)=f(x)\pm g(x)$

So, we have

$(a+b)(x)=a(x)+b(x)=(4x+9)+(3x-5) = 7x+4$

$(a-b)(x)=a(x)-b(x)=(4x+9)-(3x-5) = x+14$

As for the composition, we have to compute

$(a\circ b)(x) = a(b(x))$

So, we have to write the expression for a and evaluate it at b(x):

$a(x) = 4x+9 \implies a(b(x)) = a(3x-5) = 4(3x-5)+9 = 12x-20+9 = 12x-11$