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2 years ago

F(x) = 2x2 - 5 and g(x) = 5x + 7 Find f(g(x)) = [ ? ]x2 + [ ]x +

Mathematics

1 answer:

lbvjy [14]2 years ago

8 0

Answer:10x^2 -18

Step-by-step explanation:since f(x) is becoming the new x then youd subtitute the equation into the x of the g(x) equation. which would be 5(2x^2 -5) +7 which is 10x^2 -25 +7.and you'd simplify from there.

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“a number n equals 7 more than half the number” can be written as what

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Step-by-step explanation:

n=n/2 +7

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I need help with number 4

ss7ja [257]

Answer: Choice D

$f^{-1}(x) = (x-3)^2+2\\\\$

============================================================

Explanation:

First we replace f(x) with y. This is because both y and f(x) are outputs of a function.

To find the inverse, we swap x and y and solve for y like so

$y = \sqrt{x-2}+3\\\\x = \sqrt{y-2}+3 \ \text{ .... swap x and y; isolate y}\\\\x-3 = \sqrt{y-2}\\\\(x-3)^2 = y-2 \ \text{ ... square both sides}\\\\(x-3)^2+2 = y\\\\y = (x-3)^2+2\\\\f^{-1}(x) = (x-3)^2+2\\\\$

Note: because the range of the original function is $y \ge 3$ , this means the domain of the inverse is $x \ge 3$ . The domain and range swap roles because of the swap of x and y.

As the graph shows below, the original and its inverse are symmetrical about the mirror line y = x. One curve is the mirror image of the other over this dashed line.

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2 years ago

Read 2 more answers

1. Serena is in a math class of 20 students. Each day for a week (Monday to Friday), a student in Serena’s class is

Flauer [41]

Answer:

a) 0.05

b) 0.0526

c) 0.0625

Step-by-step explanation:

Data provided in the question:

Total number of students in a class = 20

a) since it is Monday, no student will be selected already.

Therefore,

There are 20 students from which one can be selected

Thus,

P(Serena is selected on Monday) = 1 ÷ [Number of students available]

= 1 ÷ 20

= 0.05

b) On Tuesday, one student has already been selected on Monday

Therefore,

There are (20 - 1) = 19 students from which one can be selected

Thus,

P(Serena is selected on Tuesday) = 1 ÷ [Number of students available]

= 1 ÷ 19

= 0.0526

c) On Friday , 4 student has already been selected on Monday

Therefore,

There are (20 - 4) = 16 students from which one can be selected

Thus,

P(Serena is selected on Tuesday) = 1 ÷ [Number of students available]

= 1 ÷ 16

= 0.0625

6 0

2 years ago