a) a = [tex] \frac{f (x_{1} ) - f (x_{2} )}{x_{1} - x_{2} } [/tex]
a = [tex] \frac{1/2 - 4}{- 5 - 3} [/tex]
a = [tex] \frac{- 3,5}{- 8} [/tex]
a = 7/16
Ainsi, f (x) = 7/16x + b.
On sait que f (- 5) = 1/2
7/16 * (- 5) + b = 1/2
- 35/16 + b = 1/2
b = 1/2 + 35/16
b = 43/16
Donc, f (x) = 7/16x + 43/16.
b) a = [tex] \frac{f (x_{1}) - f (x_{2)} }{x_{1} - x_{2} } [/tex]
a = [tex] \frac{- 4 - (- 4)}{3 - 5} [/tex]
a = [tex] \frac{0}{- 2} [/tex]
a = 0
Ainsi, f (x) = 0x + b
On sait que f (3) = - 4
0 * 3 + b = - 4
0 + b = - 4
b = - 4
Donc, f (x) = 0x - 4.
c) a = [tex] \frac{f (x_{1}) - f (x_{2}) }{x_{1} - x_{2} } [/tex]
a = [tex] \frac{2 - 8}{1 - 4} [/tex]
a = [tex] \frac{- 6}{- 3} [/tex]
a = 2
Ainsi, f (x) = 2x + b
On sait que f (1) = 2
2 * 1 + b = 2
2 + b = 2
b = 2 - 2
b = 0
Donc, f (x) = 2x + 0
f (x) = 2x
