Question

Дана функция y=g(x),где g(x)=x²+4x-2.Найдите: g(2x+1)сделайте пожалуйста♥

Answer 1

g(x)=x²+4x-2
g(2x+1) = (2x+1)² + 4(2x+1) - 2
= 4x² + 4x + 1 + 8x + 4 - 2
= 4x² + 12x + 5 - 2
= 4x² + 12x + 3

Answer 2

Given Function:

The given function is g(x) = x² + 4x - 2.

Finding g(2x+1):

To find g(2x+1), we substitute 2x+1 into the function g(x):

g(2x+1) = (2x+1)² + 4(2x+1) - 2

Let's simplify this expression step by step:

1. Expand the square: (2x+1)² = (2x+1)(2x+1) = 4x² + 2x + 2x + 1 = 4x² + 4x + 1 2. Distribute 4 to each term inside the parentheses: 4(2x+1) = 8x + 4

Now, substitute these simplified expressions back into the original equation:

g(2x+1) = (4x² + 4x + 1) + (8x + 4) - 2

Simplifying further:

g(2x+1) = 4x² + 4x + 1 + 8x + 4 - 2

Combining like terms:

g(2x+1) = 4x² + 12x + 3

Therefore, g(2x+1) = 4x² + 12x + 3.

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