Which pair of expressions represents inverse functions
2 answers:
Answer: C. and
Step-by-step explanation: if a function f(x) has g(x) as its inverse then it satisfies fog(x)=x and gof(x)=x
C. f(x)= and g(x)=
fog(x)=f()
=
=x
gof(x)=g()
=
=x
hence C. is the pair of inverse functions
Answer:
<h2>C.</h2>Step-by-step explanation:
When two functions are inverse of each other, their composition must fulfil the following rule.
That is, if we find their composition, the result must be the independent variable.
If you observe closely, the function given by choice C has some similarity, let's evaluate them to see if they are inverse functions.
Therefore, the pair of functions which are inverse are the given by choice C.
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<h3>Answer:</h3>
<em>Try the answers</em>
You can try the answers to see what works. You can expect all of the choices to match the first two terms, so try some farther down. Let's see if we can get -25 from -7.
a) 3*(-7) -4 = -21 -4 = -25 . . . . this one works
b) -7 -2 = -9 . . . . ≠ -25
c) -3(-7) +2 = 21 +2 = 23 . . . . ≠ -25
d) -2(-7) +1 = 14 +1 = 15 . . . . ≠ -25
The formula that works is the first one.
_____
<em>Derive it</em>
All these formulas depend on the previous term only, so we can write equations that show the required relationships. Let the unknown coefficients in our recursion formula be p and q, as in ...
Then, to get the second term from the first, we have
... 1·p +q = -1
And to get the third term from the second, we have
... -1·p +q = -7
Subtracting the second equation from the first gives ...
... 2p = 6
... p = 3 . . . . . . . this is sufficient to identify the first answer as correct
We can find q from the first equation.
... q = -1 -p = -1 -3 = -4
So, our recursion relation is ...