Question

If g(x) = 2x^2 - 4x, find g(x-3)

Answer 1

g(x - 3) = 2x² - 16x + 30

Step-by-step explanation:

To evaluate this function, I plug in (x-3):

`\sf{g(x)=2x^2-4x}`

`\sf{g(x-3)=2(x-3)^2-4(x-3)}`

`\sf{g(x-3)=2(x-3)(x-3)-4(x-3)}`

`\sf{g(x-3)=2(x^2-3x-3x+9)-4(x-3)}`

`\sf{g(x-3)=2(x^2-6x+9)-4(x-3)}`

`\sf{g(x-3)=2x^2-12x+18-4(x-3)}`

`\sf{g(x-3)=2x^2-12x+18-4x+12}`

`\sf{g(x-3)=2x^2-12x-4x+12+18}`

`\sf{g(x-3)=2x^2-16x+12+18}`

`\sf{g(x-3)=2x^2-16x+30}`

∴ answer = g(x - 3) = 2x² - 16x + 30

Answer 2

g(x-3) = 2x^2 - 16x + 30

Step-by-step explanation:

To find g(x-3), we need to substitute x-3 wherever x appears in the expression for g(x), so we have:

g(x-3) = 2(x-3)^2 - 4(x-3)

Now we need to simplify this expression using algebraic rules.

First, we can expand the square by multiplying (x-3) by itself:

g(x-3) = 2(x^2 - 6x + 9) - 4(x-3)

Next, we can distribute the 2 and the -4:

g(x-3) = 2x^2 - 12x + 18 - 4x + 12

Simplifying further, we can combine like terms:

g(x-3) = 2x^2 - 16x + 30

Therefore, g(x-3) = 2(x-3)^2 - 4(x-3) simplifies to g(x-3) = 2x^2 - 16x + 30.