Let f(x) = 5x + x2 and g(x) = 3x2 - 4x. Find f(x) * g(x)

Mathematics

2 answers:

saveliy_v [14]3 years ago

6 0

$\large \mathfrak{Solution : }$

f (x) = x² + 5x

g (x) = 3x² - 4x

f (x) * g (x) :

$( {x}^{2} + 5) \times (3 {x}^{2} - 4x)$

$3x {}^{4} - 4 {x}^{3} + 15 {x}^{2} - 20x$

gavmur [86]3 years ago

3 0

Step-by-step explanation:

f(x) × g(x)

= (x2 + 5x )× (3x2 -4x )

=3x4 + 15x3 - 4x3 -20x2

3x^4 + 11 x3 - 20x2

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What is the effect on the graph of the function f(x) = x^2 when f(x) is changed to f(x − 6)

olya-2409 [2.1K]

Answer:

The comparison graph is also attached in 3rd figure. In the 3rd figure, the graph with vertex (0, 0) is representing $f(x) = x^2$ and $\:f\left(x\right)=\left(x-6\right)^2$ is represented as being shifted 6 units to the right as compare to the function $f(x) = x^2$ .

Step-by-step explanation:

When we Add or subtract a positive constant, let say c, to input x, it would be a horizontal shift.

For example:

Type of change Effect on y = f(x)

$y = f(x - c)$ horizontal shift: c units to right

Considering the function

$f(x) = x^2$

The graph is shown below. The first figure is representing $f(x) = x^2$ .

Now, considering the function

$\:f\left(x\right)=\left(x-6\right)^2$

According to the rule, as we have discussed above, as a positive constant 6 is added to the input, so there is a horizontal shift, 6 units to the right.

The graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shown below in second figure. It is clear that the graph of $\:f\left(x-6\right)=\left(x-6\right)^2$ is shifted 6 units to the right as compare to the function $f(x) = x^2$ .