The base of the triangle is x² + 2x + 4
The height of the triangle is 2x² + 2x + 6
The area of the triangle is
A = (1/2) b h
Substituting
A = (1/2)(x² + 2x + 4)(2x² + 2x + 6)
Which can be expanded or factored
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Step-by-step explanaton:
Answer:
x^7 + 9x^2 + x + 8
Step-by-step explanation:
Combine like terms
Answer:
Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.
Step-by-step explanation:
First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y. We conclude that f is surjective.
However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.
Note:
If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.
