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2 years ago

F(x) = 4x+3x g(x) = 2x-5 7. Find (f+9) (x) 8. Find (f - g) (x)

Mathematics

1 answer:

notka56 [123]2 years ago

3 0

Answer:

7. $(f+g)(x) = 6x - 2$

8. $(f-g)(x) = 2x + 8$

Step-by-step explanation:

We are given two function, f(x) and g(x).

We want to find their addition and their subtraction, and we do this combining like terms.

The functions are:

$f(x) = 4x + 3$

$g(x) = 2x - 5$

7. Find (f+9) (x)

$4x + 3 + 2x - 5 = 4x + 2x + 3 - 5 = 6x - 2$

$(f+g)(x) = 6x - 2$

8. Find (f - g) (x)

$4x + 3 - (2x - 5) = 4x + 3 - 2x + 5 = 4x - 2x + 3 + 5 = 2x + 8$

$(f-g)(x) = 2x + 8$

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Solve 4^x-5 = 6 for x using the change of base formula log base b of y equals log y over log b

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Answer:

$4^x-5=6$ gives the solution $x=\frac{\log(11)}{\log(4)}$ .

$4^{x-5}=6$ gives the solution $x=\frac{\log(6)}{\log(4)}+5$ .

Step-by-step explanation:

I will solve both interpretations.

If we assume the equation is $4^{x}-5=6$ , then the following is the process:

$4^x-5=6$

Add 5 on both sides:

$4^x=6+5$

Simplify:

$4^x=11$

Now write an equivalent logarithm form:

$\log_4(11)=x$

$x=\log_4(11)$

Now using the change of base:

$x=\frac{\log(11)}{\log(4)}$ .

If we assume the equation is $4^{x-5}=6$ , then we use the following process:

$4^{x-5}=6$

Write an equivalent logarithm form:

$\log_4(6)=x-5$

$x-5=\log_4(6)$

Add 5 on both sides:

$x=\log_4(6)+5$

Use change of base formula:

$x=\frac{\log(6)}{\log(4)}+5$

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