Question

if f(x)=x^2+3 and g(x)=3x-1
then find the following

1a. (f+g)(x)

1b. (f+g)(3)

1c. (f-g)(x)

Answer 1

If $f(x) = x^{2} + 3$ and $g(x) = 3x - 1$ then find the following

1a. $(f + g)(x)$

1b. $(f + g)(3)$

1c. $(f - g)(x)$

**Solution:**

1a. $(f + g)(x) = f(x) + g(x) = x^{2} + 3 + 3x - 1 = x^{2} + 3x + 2$

Answer: $x^{2} + x + 2$

1b. $(f + g)(3) = (x^{2} + 3x + 2)|_{x=3} = 9 + 9 + 2 = 20$

Answer: 20

1c. $(f - g)(x) = f(x) - g(x) = x^{2} + 3 - (3x - 1) = x^{2} - 3x + 4$

Answer: $x^{2} - 3x + 4$