Question

Find the following for the function f(x) = 4x^2+3x-3

(a) f(0)
(b) f(1)
(c) f(-1)
(d) f(-x)
(e) –f(x)
(f) f(x+1)
(g) f(5x)
(h) f(x+h)

(a) f(0) = ______ (Simplify your answer)
(b) f(1) = ______ (Simplify your answer)

Answer 1

`\tt (a) f(0) = -3\\ \tt (b) f(1) = 4\\\tt (c) f(-1) = -2\\\tt (d) f(-x) = 4x^2 - 3x - 3\\\tt (e) -f(x) = -4x^2 - 3x + 3\\\tt (f) f(x+1) = 4x^2 + 11x + 4\\\tt (g) f(5x) = 100x^2 + 15x - 3\\\tt (h) f(x+h) = 4x^2 + 8xh + 4h^2 + 3x + 3h - 3`

Explanation:

Given function is f(x) = 4x^2+3x-3

We can solve the given equation by replacing or substituting the given value in place of x.

`\tt (a) f(0) = 4(0)^2 + 3(0) - 3 = -3`

`\tt (b) f(1) = 4(1)^2 + 3(1) - 3 = 4`

`\tt (c) f(-1) = 4(-1)^2 + 3(-1) - 3 = -2`

`\tt (d) f(-x) = 4(-x)^2 + 3(-x) - 3 = 4x^2 - 3x - 3`

`\tt (e) -f(x) = -(4x^2 + 3x - 3) = - 4x^2 - 3x + 3`

`\tt (f) f(x+1) = 4(x+1)^2 + 3(x+1) - 3\\ =4(x^2+2x+1) +3x+3 -3 \\=4x^2+8x+4 +3x =4x^2+11x+4`

`\tt (g) f(5x) = 4(5x)^2 + 3(5x) - 3 = 100x^2 + 15x - 3`

`\tt (h) f(x+h) = 4(x+h)^2 + 3(x+h) - 3\\ = 4(x^2 + 2xh + h^2) + 3x + 3h - 3 \\= 4x^2 + 8xh + 4h^2 + 3x + 3h - 3`