Construct a function whose reflection in the line of y=x is itself. state the symmetries of the function.

ANSWER TO PART A

The mapping for the reflection in the line , is given by

.

That is the coordinates swap position .

The only way we can construct a function , such that;

are equal is when

.

So that when .

The mapping then becomes

.

Therefore the function, is the function whose reflection in the line

is itself.

ANSWER TO PART B

The function is symmetrical with respect to the origin. That is to say the function is an odd function.

A function is symmetric with respect to the origin, if it satisfies the condition,

For instance,

Since

We say the function is symmetric with respect to the origin.

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places

2 2/3 hours duhh silly

step-by-step explanation: