Let f(x) = 4x2 + x + 1 and g(x) = x2 – 2

1 answer:

7 0

To find g (f(x)) you should substitute "4x^2+x+1" to "x" of g(x) function. You'll havew:

$g(f(x))= (4x^2+x+1)^2-2=\\ \\ =(4x^2+x)^2 +2 \cdot (4x^2+x) \cdot 1 +1^2-2= \\ \\ = 16x^4+8x^3+x^2+8x^2+2x+1-2= \\ \\ = 16x^4+8x^3+9x^2+2x-1$

To count (4x^2+x+1)^2 Just assume ( [4x^2+x] + 1)^2 and use the (a+b)^2=a^2+2ab+b^2 formula, where a=4x^2+x and b=1

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Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 40, \sigma = 2$