Mathematics, 27.10.2019 05:43 valenciafaithtorres

Which function has an inverse function?
/=means the _ of a fraction like 4
_
5
f(x)= [x+3]/5

f(x)=x^5-3

f(x)=x^4/7 +27

f(x)=1/x^2

$Which function has an inverse function? /=means the _ of a fraction like 4 _ 5$

Answers: 2

Show answers

Answers

Answer from: 22swittman

The correct option is 2.

Step-by-step explanation:

A function has an inverse function if and only if it is a one-to-one function. It means for each value of x there exist a unique value of y.

In option 1,

$f(x)=\frac{|x+3}}{5}$

It is an absolute function. For each value of x there axis more than 1 value of f(x). Therefore this function does not has an inverse function.

In option 2,

F(x)=x^5-3

The degree of the function is 5 which is an odd number. Therefore it is a one-to-one function. Therefore this function has an inverse function.

In option 3,

$F(x)=\frac{x^4}{7}+27$

The degree of the function is 4 which is an even number. Therefore it is not a one-to-one function. Therefore this function does not has an inverse function.

In option 4,

$F(x)=\frac{1}{x^2}$

The degree of the function is 2 which is an even number. Therefore it is not a one-to-one function. Therefore this function does not has an inverse function.

Hence option 2 is correct.

Answer from: Quest

c. x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

$\frac{little}{big} =\frac{side mn}{side ab}=\frac{side on}{side cb}$ .