Question

Express the function h(x)=(x+1)^4 in the form of. If (x)=x^4, find the function g(x).

Answer 1

To express the function h(x) = (x+1)^4 in the form of g(x) = x^4, we can expand and simplify the expression.

Using the binomial theorem, we can expand (x+1)^4 as follows:

(x+1)^4 = 1*C(4,0)*x^4 + 4*C(4,1)*x^3*1 + 6*C(4,2)*x^2*1^2 + 4*C(4,3)*x^1*1^3 + 1*C(4,4)*1^4

Simplifying each term:

(x+1)^4 = 1*x^4 + 4*x^3 + 6*x^2 + 4*x + 1

Therefore, the function g(x) = x^4 is equivalent to h(x) = (x+1)^4 expressed in the expanded form.

Explanation: