Question

How solve this question with explanation ??

Answer 1

Answer:

Step-by-step explanation:

First of all the quality of picture is bad!!! Impossible to see anything...

I know what this task all about, but still need to operate clear picture...

So, g(x) = 5x² + 3 and h(x) = 7x - 4 are functions R ---> R

a). (I assume there is sign of multiplication between g and h)

g*h = (5x² + 3)(7x - 4) = 35x³ - 20x² + 21x - 12

b). Is g (????) ? Sorry, but I cannot recognize the word.

No, g(x) is not one-to-one function. Each "x" in the domain has only one "y" image in the range, but "y" in the range has two "x" in the domain.

c). Function $g^{-1}$ is not exist in whole set of real numbers.

g = 5x² + 3 ⇒ x² = $\frac{g-3}{5}$ ⇒ x = $\sqrt{\frac{g-3}{5} }$ ⇒ $g^{-1}$(x) = $\sqrt{\frac{x-3}{5} }$ ( x ≥ 3 and $g^{-1}$ ≥ 0 )

Domain of $g^{-1}$ is [ 3 , ∞ ) ;

Range of $g^{-1}$ is [0 , ∞ ) .

d). h(x) = 7x - 4 ⇒ $h^{-1}$ = $\frac{x+4}{7}$ is R ---> R function.