Answer with explanation:
≡≡It is given that , function, f, passes through the points (1,1), (2,7) and (3,25).
Slope between two points is given by the formula
[tex]=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \text{Having coordinates} ,(x_{1},y_{1}),(x_{2},y_{2})[/tex]
→→You will find that,
[tex]\frac{7-1}{2-1}=6, \text{and} \frac{25-7}{3-2}=18 \text{and} \frac{25-1}{3-1}=12[/tex]
The slopes are not same.So, the given function is not linear.
Also, f(1)=1, f(2)=7,f(3)=25
1+6=7+18=25,f(x) increases each time differently ,first by a number of ,6 ,then by 18,may be then by 54,....with increase in value of x , by 1 unit.
≡≡The function, g, passes through the points (1,36), (2,43) and (3,50).
Slope between two points is
[tex]\frac{43-36}{2-1}=\frac{50-43}{3-2}=\frac{50-36}{3-1}=7[/tex]
36 +7=43+7=50+7=57
So,the function is linear.
f(x) increases each time with same digit,that is by value of 7, with increase in value of x , by 1 unit.
Option C:⇒As the value of x increases, the value of f(x) will eventually exceed the value of g(x).
