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.
e follSOLUTION
Given the question in the image, the following are the solution steps to answer the question
STEP 1: Write the general equation of an ellipse
STEP 2: Identify the parameters
the length of the major axis is 2a
the length of the minor axis is 2b
STEP 3: Get the equation of the ellipse
STEP 4: Pick the nearest equation from the options,
Hence, the equation of the ellipse in the image is given as:
OPTION A
Answer:
√
15 +
√
10
Step-by-step explanation:
The answer is above
