Explain how you could use the formula

Mathematics

1 answer:

Ugo [173]4 years ago

6 0

Answer:

x=3,-8

Step-by-step explanation:

$x^2+5x=24\\add ~both~sides~(\frac{5}{2})^2\\x^2+5x+(\frac{5}{2})^2=24+\frac {25}{4}\\(x+\frac{5}{2})^2=\frac{96+25}{4}\\(x+\frac{5}{2})^2=\frac{121}{4}\\x+\frac{5}{2}=\pm \frac{11}{2}\\x=-\frac{5}{2} \pm \frac{11}{2} \\either~x=-\frac{5}{2} +\frac{11}{2} =\frac{6}{2} =3\\or~x=-\frac{5}{2} -\frac{11}{2} =-\frac{16}{2} =-8$

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If g(x) is the inverse of f(x), what is the value of f(g(2))?

Elan Coil [88]

Answer:

Step-by-step explanation:

So to figure this out we just need to flip the values of x and y in the table and then redefine that as the function g(x), because an inverse is essentially the reverse!

So if we flipped x and y's for f(x). We would see that our output or y of g(x) is -3 when x = 2, or in other words g(2) = -3. This means that we are now going to solve for when f(-3). So now lets look at the table and find the value at x = -3 for f(x). This value is 2, so the value of f(g(2)) = 2.

*In the future*

When you have a composite function of two inverses they essentially cancel out and would leave whatever the value of x is. So if we know f(x) and g(x) were inverses the value of f(g(2)) would just be 2.

For example:

ln(x) and e^x are inverses so if I had a composition like this:

$e^{ln(2)}$