Answer:
y = 4x + 32
Step-by-step explanation:
Given: Temperature at sunrise = 32°F
y is the temperature after x hours of sunrise
Temperature change is 4°F/hour.
The equation of a line in slope intercept form is given by
y = mx +c
where m is the slope, which is the change in value of y to the value of x
and c is the value of y at x = 0
At sunrise, x =0 and y =32
∴ c = 32
Also we see that the change in temperature to that of time is 4/1 = 4
∴ m = 4
Substituting the values of m and c in the equation of line, we have
y = 4x +32
Answer: its option 3 I just did the test right now
Step-by-step explanation:
![\bf \begin{cases} f(x)=\sqrt[3]{7x-2}\\\\ g(x)=\cfrac{x^3+2}{7} \end{cases}\\\\ -----------------------------\\\\ now \\\\ f[\ g(x)\ ]\implies f\left[ \frac{x^3+2}{7} \right]\implies \sqrt[3]{7\left[ \frac{x^3+2}{7} \right]-2}\implies \sqrt[3]{x^3+2-2} \\\\\\ \sqrt[3]{x^3}\implies x\\\\ -----------------------------\\\\ or \\\\ g[\ f(x)\ ]\implies g\left[\sqrt[3]{7x-2}\right]\implies \cfrac{\left[\sqrt[3]{7x-2}\right]^3+2}{7} \\\\\\ \cfrac{7x-2+2}{7}\implies \cfrac{7x}{7}\implies x](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Af%28x%29%3D%5Csqrt%5B3%5D%7B7x-2%7D%5C%5C%5C%5C%0Ag%28x%29%3D%5Ccfrac%7Bx%5E3%2B2%7D%7B7%7D%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0Anow%0A%5C%5C%5C%5C%0Af%5B%5C%20g%28x%29%5C%20%5D%5Cimplies%20f%5Cleft%5B%20%5Cfrac%7Bx%5E3%2B2%7D%7B7%7D%20%5Cright%5D%5Cimplies%20%5Csqrt%5B3%5D%7B7%5Cleft%5B%20%5Cfrac%7Bx%5E3%2B2%7D%7B7%7D%20%5Cright%5D-2%7D%5Cimplies%20%5Csqrt%5B3%5D%7Bx%5E3%2B2-2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Csqrt%5B3%5D%7Bx%5E3%7D%5Cimplies%20x%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0Aor%0A%5C%5C%5C%5C%0Ag%5B%5C%20f%28x%29%5C%20%5D%5Cimplies%20g%5Cleft%5B%5Csqrt%5B3%5D%7B7x-2%7D%5Cright%5D%5Cimplies%20%5Ccfrac%7B%5Cleft%5B%5Csqrt%5B3%5D%7B7x-2%7D%5Cright%5D%5E3%2B2%7D%7B7%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7B7x-2%2B2%7D%7B7%7D%5Cimplies%20%5Ccfrac%7B7x%7D%7B7%7D%5Cimplies%20x)
thus f[ g(x) ] = x indeed, or g[ f(x) ] =x, thus they're indeed inverse of each other
X = -3, y = 2 rise over run
