Simplify f+g / f-g when f(x)= x-4 / x+9 and g(x)= x-9 / x+4
2 answers:
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Answer:
a) f(x) = x² -9
function is an even function
b) g(x) = |x -3|
function is an even function
c) f(x)= x / x²-1
function is odd function
d) g(x) = x + x²
Given function is not an even not odd function
This function is neither even or odd
Step-by-step explanation:
<u><em>Explanation</em></u>:-
a) Given f(x) = x² -9
<u><em>Even function </em></u>
If f(-x) = f(x) , then the function is even function.
f(-x) = (-x)² -9
= x² -9
= f(x)
f(-x) = f(x)
∴ Given function is an even function
b)
Given g(x) = |x -3|
<u><em>Even function </em></u>
If g(-x) = g(x) , then the function is even function.
g(-x) = |-(x-3)|
= |x-3|
g(-x) = g(x)
∴ Given function is an even function
c)
<u><em>odd function</em></u>
If f(-x) =- f(x) , then the function is odd function.
f(-x) =
= -f(x)
f(-x) = -f(x)
∴ Given function is odd function
d)
If g(-x) = g(x) , then the function is even function.
g(x) = x + x²
g(-x) = -x + (-x)²
= - (x - x²)
This is not either even or odd function
∴ Given function is neither function
Step-by-step explanation: The place value chart can help us write a number in expanded notation. When we put 2,930,365 into the place value chart, we can recognize that our number is equal to 2 millions + 9 hundred thousands + 3 ten thousands + 0 thousands + 3 hundreds + 6 tens + 5 units.
The place value chart is attached in the image provided.
