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3 years ago

If f(x)=3^x+10 and g(x)=2x-4, find (f-g)(x)

Mathematics

1 answer:

nataly862011 [7]3 years ago

6 0

<h3>Answer: 3^x - 2x + 14</h3>

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

Work Shown:

(f - g)(x) = f(x) - g(x)

(f - g)(x) = ( f(x) ) - ( g(x) )

(f - g)(x) = ( 3^x + 10 ) - ( 2x-4 )

(f - g)(x) = 3^x + 10 - 2x+4

(f - g)(x) = 3^x - 2x + (10+4)

(f - g)(x) = 3^x - 2x + 14

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Step-by-step explanation:

In this problem we have:

$d_1=1 mi$ is the distance travelled during the 1st day

$d_2=1.3 mi$ is the distance travelled during the 2nd day

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$d_4=3.1 mi$ is the distance travelled during the 4th day

We notice that the difference between the distance travelled on the (n+1)-th day and the distance travelled on the n-th day doubles every day. In fact:

$d_2-d_1=0.3\\d_3-d_2=2\cdot 0.3 = 0.6\\d_4-d_3=2\cdot 0.6 = 1.2$

Which can be rewritten using the general formula:

$d_{n+1}-d_n=2(d_n-d_{n-1})$

This means that

$d_{n+1}=d_n+2(d_n-d_{n-1})$

By applying this formula recursively, we can find the 7th term, which is the distance travelled on the 7th day:

$d_1=1\\d_2=1.3\\d_3=1.9\\d_4=3.1\\d_5=3.1+2\cdot 1.2=5.5\\d_6=5.5+2\cdot 2.4=10.3\\d_7=10.3+2\cdot 4.8=19.9 mi$

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3 years ago

Math help please Let f(x)=x2+5 and g (x)=3x+4; find (g o f)(7); (g o f)(7)=; help me solve!! Please!

lorasvet [3.4K]

f(x) = 2x

g(x) = x + 3

First let us find (fog)(x)

(fog)(x) = f(g(x)

= f(x+3)

= 2(x+3)

= 2x + 6

==> (fog)(x) = 2x + 6

Now let us find (gof)(x):

(gof)(x) = g(f(x)

= g(2x)

= 2x + 3

==> <span>(gof)(x) = 2x + 3</span>

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2 years ago

(x^3+10x^2+2)/(x+10)

SCORPION-xisa [38]

The quotient is x^2

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Step-by-step explanation:

We need to divide: $\frac{\left(x^3+10x^2+2\right)}{x+10}$

The division is shown in figure attached.

The quotient is x^2

The remainder is 2

Keywords: Division of polynomials

Learn more about Division of polynomials at:

#learnwithBrainly

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2 years ago