if the given function is f(x) = x^4+2x^3-x+1g(x)=x+1 then F(g(x))?​

F(g(x)) = x⁴ + 6x³ + 12x² + 9x + 3

Answered by cervantesmaryjoy187 | 2024-10-20

Answer:Here's how to find F(g(x)): 1. Understand the Composition of Functions The notation F(g(x)) means we're going to substitute the entire function g(x) into the function F(x) wherever we see an 'x'. 2. Substitute g(x) into F(x) - F(x) = x⁴ + 2x³ - x + 1- g(x) = x + 1 Substitute (x + 1) for every 'x' in F(x): F(g(x)) = (x + 1)⁴ + 2(x + 1)³ - (x + 1) + 1 3. Expand and Simplify Now, we need to expand and simplify the expression: - (x + 1)⁴ = x⁴ + 4x³ + 6x² + 4x + 1 (You can use the binomial theorem or expand it step-by-step)- 2(x + 1)³ = 2(x³ + 3x² + 3x + 1) = 2x³ + 6x² + 6x + 2 Substitute these expanded terms back into the expression: F(g(x)) = (x⁴ + 4x³ + 6x² + 4x + 1) + (2x³ + 6x² + 6x + 2) - (x + 1) + 1 4. Combine Like Terms Combine all the terms with the same powers of 'x': F(g(x)) = x⁴ + 6x³ + 12x² + 9x + 3 Therefore, F(g(x)) = x⁴ + 6x³ + 12x² + 9x + 3Step-by-step explanation: pa brainliest po thanks

Answered by ganancialj76 | 2024-10-20