Questions: Given g(x)=4x^2-x+9, find the following. (a) g(0) (b) g(-1) (c) g(r) (d) g(x+h)

Transcript text: Given $g(x)=4 x^{2}-x+9$, find the following. (a) $g(0)$ (b) $g(-1)$ (c) $g(r)$ (d) $g(x+h)$

Solution

Step 1: Evaluate $ g(0) $

To find $ g(0) $, we substitute $ x = 0 $ into the function $ g(x) = 4x^2 - x + 9 $:

\[ g(0) = 4(0)^2 - 0 + 9 = 9 \]

Step 2: Evaluate $ g(-1) $

To find $ g(-1) $, we substitute $ x = -1 $ into the function $ g(x) = 4x^2 - x + 9 $:

\[ g(-1) = 4(-1)^2 - (-1) + 9 = 4(1) + 1 + 9 = 4 + 1 + 9 = 14 \]

Step 3: Evaluate $ g(r) $

To find $ g(r) $, we substitute $ x = r $ into the function $ g(x) = 4x^2 - x + 9 $:

\[ g(r) = 4r^2 - r + 9 \]

\[ \boxed{g(0) = 9} \] \[ \boxed{g(-1) = 14} \] \[ \boxed{g(r) = 4r^2 - r + 9} \]

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