Question

Determine whether each of these functions is a bijection from R toR. a) f(x) = -3x + 4 b) f(x) = -3x2 +7 c) f(x) = (x+1)/(x+2) d) f(x) = x5 +1"

Answer 1

Answer:

36 is right answer of your question

Answer 2

Given:

a) f(x) = -3x + 4 b) f(x) = -3x2 +7 c) f(x) = (x+1)/(x+2) d) f(x) = x5 +1

each of these functions is a bijection from R to R.

(a) f(x) = -3x + 4

f(x)=f(y)

-3x+4=-3y+4

x=y

Hence the function is bijection

(b) -3x²+7

f(-x)=f(x)

Hence the function is not bijection

(c)  f(x) = (x+1)/(x+2)

$f(x)=\frac{x+1}{x+2}=1$

Here is no real number.

Hence the function is not bijection.

(d) $x^{5}+1$

It is a increasing function.

Hence the function is bijection.

(a) Hence the function is bijection.

(b) Hence the function is not bijection.

(c) Hence the function is not bijection.

(d) Hence the function is bijection.