For f(x) = 3x +1 and g(x) = x^2-6, find (1-3)(x).

Mathematics

1 answer:

r-ruslan [8.4K]3 years ago

6 0

Answer:

Observe that (fog)(x) is equivalent to f(g(x)) which is to say intuitively the output of the function g(x) is fed as an input into the function f(x).

So in this case the general output of g(x) is x^2-6 for every input x. Thus fed as an input of f(x) in the form f(x^2-6) becomes 3(x^2-6)+1=3x^2-17.

Step-by-step explanation:

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ahrayia [7]

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#Indian : )

6 0

3 years ago

Write the following number as ratios of integers

s2008m [1.1K]

Our goal here is to somehow "surgically remove" the repeating part of the number, so let's start by putting the original value in a variable and messing around with it a bit.

We'll let $x=7.\overline{6}$ . We want to cut the $0.\overline{6}$ bit off completely, so let's create the scalpel that'll let us do that. If $x=7.\overline{6}$ , then we can also say that $10x=76.\overline{6}$ . Maybe I was lying a bit: the $x$ is our real scalpel here, and $10x$ is where we'll be making the cut. Mathematically, a "cut" is almost always shorthand for subtraction, so let's see what our operation (cutting $x$ off of $10x$ ) leaves us with:

$10x-x=76.\overline{6}-7.\overline{6}\\9x=69$

The operation was a success! We can now simply divide either side by 9 to find $x = 69/9$ , which, when reduced by dividing the numerator and denominator by 3, gives us $x=23/3$