Questions: Given that g(x)=2x^2-2x+2, find each of the following. a) g(0) b) g(-1) c) g(4) d) g(-x) e) g(1-t)

Transcript text: Given that $\mathrm{g}(\mathrm{x})=2 \mathrm{x}^{2}-2 \mathrm{x}+2$, find each of the following. a) $g(0)$ b) $g(-1)$ c) $g(4)$ d) $g(-x)$ e) $g(1-t)$

Solution

Solution Steps

To solve the given problems, we need to evaluate the function $ g(x) = 2x^2 - 2x + 2 $ at specific values of $ x $.

a) For $ g(0) $, substitute $ x = 0 $ into the function. b) For $ g(-1) $, substitute $ x = -1 $ into the function. c) For $ g(4) $, substitute $ x = 4 $ into the function.

Step 1: Evaluate $ g(0) $

To find $ g(0) $, substitute $ x = 0 $ into the function $ g(x) = 2x^2 - 2x + 2 $: \[ g(0) = 2(0)^2 - 2(0) + 2 = 2 \] \[ \boxed{g(0) = 2} \]

Step 2: Evaluate $ g(-1) $

To find $ g(-1) $, substitute $ x = -1 $ into the function $ g(x) = 2x^2 - 2x + 2 $: \[ g(-1) = 2(-1)^2 - 2(-1) + 2 = 2(1) + 2 + 2 = 6 \] \[ \boxed{g(-1) = 6} \]

Step 3: Evaluate $ g(4) $

To find $ g(4) $, substitute $ x = 4 $ into the function $ g(x) = 2x^2 - 2x + 2 $: \[ g(4) = 2(4)^2 - 2(4) + 2 = 2(16) - 8 + 2 = 32 - 8 + 2 = 26 \] \[ \boxed{g(4) = 26} \]